Advertisements
Advertisements
Question
ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.
Prove that
(i) BG = CH
(ii) AG = AH
Advertisements
Solution
In ΔABC
AB = AC
∠ABC = ∠ACB ...(equal sides have equal angles opposite to them)...(i)
∠GBC = ∠HCB = 90° ........(ii)
Subtracting (i) from (ii)
∠GBA = ∠HCA..........(iii)
In ΔGBA and ΔHCA
∠GBA = ∠HCA ...(from iii)
∠BAG - ∠CAH ...(vertically opposite angles)
BC = BC
Therefore, ΔGBA ≅ ΔHCA ...(ASA criteria)
Hence, BG = CH and AG = AH.
APPEARS IN
RELATED QUESTIONS
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(DF)`
If ΔABC ≅ ΔABC is isosceles with
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
In the given figure, AB ⊥ BE and FE ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to
In the given figure, seg AB ≅ seg CB and seg AD ≅ seg CD. Prove that ΔABD ≅ ΔCBD.
In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
State, whether the pairs of triangles given in the following figures are congruent or not:
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
In the figure, BC = CE and ∠1 = ∠2. Prove that ΔGCB ≅ ΔDCE.
In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.
